With the support of American Vogue editor Anna Wintour and the catwalk queen of va-va voom Donatella Versace, Glasgow-born designer Christopher Kane, at just 27, has become one of London fashion week's biggest names. And he's also set to be one of the hottest draws on the high street. Next Friday, to coincide with London fashion week's 25th anniversary, Topshop will unveil the designer's third and largest high-street collection of clothes and accessories. Kane's winning mix of body-con dresses, tough platforms and embellished pieces are likely to spend limited time on the shop floor. Similarly, his debut range of accessories for Versus (a Versace spin-off), which also launches this season, has already gained waiting-list status.

If the name leaves you blank, it is perhaps because, unlike many of his contemporaries, Kane doesn't court celebrities. In 2007, he was quoted as saying that he hadn't lent Victoria Beckham a dress when requested because he didn't like her. "She's not the kind of woman I think about when I'm designing my collection. Plus, I'm hardly in the financial position to be giving clothes away to somebody so wealthy." Clearly he didn't need the endorsement of Posh Spice to draw attention to his label. In recent months, Yasmin le Bon, Rihanna and Emma Watson have all been photographed in his frocks.

Such A-list gloss is in short supply as I arrive at the door of Kane's studio in Dalston, east London. Sitting behind a desk, in a simple navy cardigan and jeans, the designer is unassuming, playing down the buzz around him – buzz that started with his catwalk debut in September 2006. The series of neon micro mini frocks (or, as they were soon to be dubbed, "body-con dresses") on display that day, with their ruffled inserts, snappy little belts and crystal bauble zips, made the fashion pack sit up and take note. Among them was Wintour, who met with him that very same day. "She smelled really good and looked immaculate in a Prada dress with gorgeous jewellery," he recalls in a soft Glaswegian lilt. "I was in scruffy jeans and stinking."

Despite Wintour's frosty reputation, Kane describes her as "down to earth" and "focused". They now regularly meet in Paris where he presents his ideas to her. Known for her industry clout and matchmaking skills (Wintour often sets up new designers with established brands), she introduced Kane to Donatella Versace backstage at one of her shows. A week later, Versace invited him to work with her in Milan. He declined, wanting to focus on developing his own label, but accepted a consulting role. It has gone on to be a hugely successful partnership. "He's a good fit with Versace," says Harriet Quick, fashion features director of British Vogue, "because of their shared body-con, rock-heroine image, which is always deeply respectful of womankind."

"Donatella is a great boss," says Kane. "She walks in a room and you are transfixed. You just want to hang out with her all the time. So much stuff she wants to tell you, and so much you want to ask her." The appreciation is mutual, with Versace comparing Kane's energy with that of her brother Gianni (who set up the label) – a compliment that Kane typically shrugs off. "Gianni is legendary," he says. "When you look at his archive, it's unbelievable."

Kane has come a long way from his roots, but he says that Gianni Versace and TV's The Clothes Show were a great inspiration to him when he was growing up. "When you live in Scotland you don't go out much, it's as dull as a cardboard box," he says. Surrounded by women, his mother and her sisters, and his own sisters (his father died at 60), he rarely spent time with other kids. Perhaps it is not surprising that he has ended up working closely with one of his sisters, Tammy, who studied at the Scottish College of Textile Design. It's an intensely creative relationship that sees them working closely on every collection. But Kane dismisses the idea that Tammy is any kind of muse. "I live in Dalston, not the Champs-Elysée."

They are a canny pair. Each season, between them, they create back stories for the collections that they think will tickle the media. "A few weeks before the show, we come up with ideas for the press about how we see the collection," says Kane. Collections are given myriad reference points. For example, the Planet of the Apes, the Flintstones and Raquel Welch in One Million Years BC were all themes for spring/summer 2009's collection, which featured animal-print knits and 3D scalloped-edged leather pieces.

Similarly clever is the way Kane's designs seem to shift gear each season, while still retaining the signatures – from the mixing of hard and soft fabrics, to ruffles and embellishment – which are crucial in developing a unique and recognisable brand. "He manages to define a moment each season, which is very hard to do. His delicate dresses, bomber jackets, cashmeres and T-shirts are now solid parts of his lexicon," says Quick.

This distinct handwriting can be seen in his new Topshop collection. Of the 39 pieces, most feature some kind of embellishment, from rivets in denim to mirrors or eyelets on a variety of black or neon dresses and tops. Oversized gems decorate and trace the necklines of dresses. Even a grey marl tracksuit ("I like the idea of making ugly pretty," says Kane) has been given the Kane remix. It is almost a collection of his greatest hits.

So what next for Kane? The fashion spotlight is famously harsh and fleeting. It's a pressure that Kane says is getting bigger every season, though he concedes it helps to keep him focused. He says the idea of his own Bond Street store anytime soon makes him feel sick. His own fashion house, though, surely festooned in gold, à la Versace, slap bang in the middle of east London, is, he laughs, something to aim for. e